Also, I don't know how you can claim Hebrew is phonetically represented by its alphabet rather than the other way around, as a revived language the pronunciations are largely a matter of convention based on Yiddish. It would be more accurate to say that modern Hebrew uses an ancient writing system, which happens to be closely related to the ancestor of modern European alphabets.
See https://en.wikipedia.org/wiki/Revival_of_the_Hebrew_language
Also, not all colloquial dialects are mutually intelligible. Different Chinese dialects are still often referred to as "dialects," despite not being mutually intelligible (e.g. Cantonese vs Mandarin). While that's typically mostly the case for Western languages, there's a spectrum even there.
Of course, because modern Hebrew was constructed based on (the modern understanding of) Biblical Hebrew around the 1920s or slightly earlier, whereas Modern English naturally evolved for ~400 years from Shakespearean English and other forms of English.
Linguists elide over the whole thing by using the term “language variety.”
I dunno, some English dialects don't seem particularly intelligible to me, and I'm a natively fluent speaker of it.
That said, two people who understand each other are, by any reasonable definition, speaking dialects of the same tongue (if not, obviously, the very same dialect).